Calculus Review

Optional Reading
Author

Meike Niederhausen

Published

September 23, 2023

Modified

July 31, 2023

Introduction

Calculus will be used in probability throughout the quarter, as well as in the following math stat classes. Below are topics and links from Paul’s Online Math Notes to help you review algebra and calculus skills that are essential to BSTA 550.

  • You can ignore all examples that use trigonometry.

  • I listed the sections that you should be familiar with. The webpages have both notes and exercises for you to practice.

  • I recommend first reviewing the italicized sections since we will be using series early in the course.

  • We will not use differentiation and integration until the second half of the course (Week 6), so you have some time to review.

Topics

  • Algebra

  • Calculus 1   [Notes]   [Practice Problems]

    • Derivatives

      • Differentiation Formulas

      • Product and Quotient Rule

      • Derivatives of Exponential and Logarithm Functions (Only need exponential functions, and in particular only ex)

      • Chain Rule

    • Integrals

      • Indefinite Integrals

      • Computing Indefinite Integrals

      • Substitution Rule for Indefinite Integrals

      • More Substitution Rule

      • Area Problem

        • Don’t worry about the computations. Read through as a review for how integrals calculate area under the curve as the limit of areas of rectangles.

      • The Definition of the Definite Integral

      • Computing Definite Integrals

      • Substitution Rule for Definite Integrals

    • Applications of Integrals

      • Area Between Curves

    • Extras

      • Summation Notation

  • Calculus 2   [Notes]   [Practice Problems]

    • Integration Techniques

      • Integration by Parts

    • Sequences and Series

      • Series - The Basics

      • Series - Special Series (just Geometric Series)